What if everyone who took the SAT guessed on every multiple-choice question? How many perfect scores would there be?

—Rob Balder

None.

The SAT is a standardized test given to high school students (similar to
the ACT). The scoring is such that under certain circumstances, guessing
an answer can be a good strategy. But what if you guessed on everything?

Not all of the SAT is multiple-choice, so let’s focus on the multiple
choice questions to keep things simple. We’ll assume everyone gets the
essay questions and fill-in-the-number sections correct.

There are 44 multiple-choice questions in the math (quantitative)
section, 67 in the critical reading (qualitative) section, and 47 in the
newfangled writing section. Each question has five options, so a random
guess has a 20% chance of being right:

If all four million 17-year-olds all took the SAT, and they all guessed
randomly, it’s a statistical certainty that there would be no perfect
scores on any of the three sections.

How certain is it? Well, if they each used a computer to take the test a
million times each day, and continued this every day for five billion
years—until the Sun expanded to a red giant and the Earth was charred to
a cinder—the chance of any of them ever getting a perfect score on just
the math section would be about 0.0001%.

This means that the odds of acing the SAT by guessing are worse than the
odds of every living ex-President and every member of the main cast of
Firefly all being independently struck by lightning … on the same day.

(Everyone survives but Alan Tudyk and Ron Glass)

To everyone taking the SAT this year, good luck—but it won’t be enough.